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In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
A Course of Mathematics: In Three Volumes : Composed for the Use of the ... - Page 63
by Charles Hutton - 1811

## Tables of Logarithms of Numbers and of Sines and Tangents for Every Ten ...

Elias Loomis - 1859 - 372 pages
...BxBC, or sin. A : sin. B : : BC : AC. THEOREM II. (50.) In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference. Let ABC be any triangle ; then will...

## Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - 1860 - 472 pages
...it may be shown that §«.] TRIGONOMETRY. THEOREM It In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the op? posite angles is to the tangent of half their difference. By Theorem I., we have o : c : :...

## Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 pages
...demonstrated that AB : BC = sin. C : sin. A. PROPOSITIOK VI. THEOREM. The sum of two sides of a triangle is to their difference as the tangent of half the sum of the angles at the base to the tangent of half their difference. Let ABC be any triangle, then if B...

## Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 714 pages
...=2 tan 2 A. 5. In any triangle, calling one side the base, prove that the sum of the other two sides is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference. 6. Observers on two ships a mile...

## Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 518 pages
...__ cot ^ (A — B) f(\7\ sin A — sin B ~ wt~i (A + B) ; ( ' that is, The sum of the sines of two angles is to their difference as the tangent of half the sum of the angles is to the tangent of half their difference, or as the cotangent of half their difference...

## Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1861 - 638 pages
...B _ cot ^ (A — B) tf"\ sin A — sin B ~~ coti (A + B) ' ( ' that is, The sum of the sines of two angles is to their difference as the tangent of half the sum of the angles is to the tangent of half their difference, or as the cotangent of half their difference...

## Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1863 - 504 pages
...sin B _ cot | (A — B) . . sin "A ^^sin "B ~ cot ±1 (A^~B) ' that is, The sum of the sines of two angles is to their difference as the tangent- of half the sum of the angles is to the tangent of half their difference, or as the cotangent of half their difference...

## Elements of Plane Trigonometry: And Their Application to the Measurement of ...

William Frothingham Bradbury - 1864 - 324 pages
...the first proportion in Theorem I. THEOREM III. 41. In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference. Let ABC be a triangle ; then AB + BC:BC—...